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Question
Find the domain for which the functions f(x) = 2x2 – 1 and g(x) = 1 – 3x are equal.
Solution
For f(x) = g(x)
⇒ 2x2 – 1 = 1 – 3x
⇒ 2x2 + 3x – 2 = 0
⇒ 2x2 + 4x – x – 2 = 0
⇒ 2x(x + 2) – 1(x + 2) = 0
⇒ (2x – 1)(x + 2) = 0
Thus domain for which the function f(x) = g(x) is `{1/2, -2}`.
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